Matroids with nine elements

We describe the computation of a catalogue containing all matroids with up to nine elements, and present some fundamental data arising from this cataogue. Our computation confirms and extends the results obtained in the 1960s by Blackburn, Crapo and Higgs. The matroids and associated data are stored in an online database, and we give three short examples of the use of this database.Comment: 22 page

Sample and Filter: Nonparametric Scene Parsing via Efficient Filtering

Scene parsing has attracted a lot of attention in computer vision. While parametric models have proven effective for this task, they cannot easily incorporate new training data. By contrast, nonparametric approaches, which bypass any learning phase and directly transfer the labels from the training data to the query images, can readily exploit new labeled samples as they become available. Unfortunately, because of the computational cost of their label transfer procedures, state-of-the-art nonparametric methods typically filter out most training images to only keep a few relevant ones to label the query. As such, these methods throw away many images that still contain valuable information and generally obtain an unbalanced set of labeled samples. In this paper, we introduce a nonparametric approach to scene parsing that follows a sample-and-filter strategy. More specifically, we propose to sample labeled superpixels according to an image similarity score, which allows us to obtain a balanced set of samples. We then formulate label transfer as an efficient filtering procedure, which lets us exploit more labeled samples than existing techniques. Our experiments evidence the benefits of our approach over state-of-the-art nonparametric methods on two benchmark datasets.Comment: Please refer to the CVPR-2016 version of this manuscrip

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

Nonlinear Matroid Optimization and Experimental Design

We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oracle-presented matroids, that makes repeated use of matroid intersection, and an algebraic algorithm for vectorial matroids. Our work is partly motivated by applications to minimum-aberration model-fitting in experimental design in statistics, which we discuss and demonstrate in detail

Adaptive beamforming for large arrays in satellite communications systems with dispersed coverage

Conventional multibeam satellite communications systems ensure coverage of wide areas through multiple fixed beams where all users inside a beam share the same bandwidth. We consider a new and more flexible system where each user is assigned his own beam, and the users can be very geographically dispersed. This is achieved through the use of a large direct radiating array (DRA) coupled with adaptive beamforming so as to reject interferences and to provide a maximal gain to the user of interest. New fast-converging adaptive beamforming algorithms are presented, which allow to obtain good signal to interference and noise ratio (SINR) with a number of snapshots much lower than the number of antennas in the array. These beamformers are evaluated on reference scenarios

Fast space-variant elliptical filtering using box splines

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based on a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using pre-integration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based on the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.Comment: 12 figures; IEEE Transactions on Image Processing, vol. 19, 201